{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Table of Contents](./table_of_contents.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ensemble Kalman Filters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <style>\n",
       "        .output_wrapper, .output {\n",
       "            height:auto !important;\n",
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       "        .output_scroll {\n",
       "            box-shadow:none !important;\n",
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       "        }\n",
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       "    "
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      "text/plain": [
       "<IPython.core.display.HTML object>"
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     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#format the book\n",
    "import book_format\n",
    "book_format.set_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> I am not well versed with Ensemble filters. I have implemented one for this book, and made it work, but I have not used one in real life. Different sources use slightly different forms of these equations. If I implement the equations given in the sources the filter does not work. It is possible that I am doing something wrong. However, in various places on the web I have seen comments by people stating that they do the kinds of things I have done in my filter to make it work. In short, I do not understand this topic well, but choose to present my lack of knowledge rather than to gloss over the subject. I hope to master this topic in the future and to author a more definitive chapter. At the end of the chapter I document my current confusion and questions. In any case if I got confused by the sources perhaps you also will, so documenting my confusion can help you avoid the same.\n",
    "\n",
    "\n",
    "The ensemble Kalman filter (EnKF) is very similar to the unscented Kalman filter (UKF) of the last chapter. If you recall, the UKF uses a set of deterministically chosen weighted sigma points passed through nonlinear state and measurement functions. After the sigma points are passed through the function, we find the mean and covariance of the points and use this as the filter's new mean and covariance. It is only an approximation of the true value, and thus suboptimal, but in practice the filter is highly accurate. It has the advantage of often producing more accurate estimates than the EKF does, and also does not require you to analytically derive the linearization of the state and measurement equations. \n",
    "\n",
    "The ensemble Kalman filter works in a similar way, except it uses a *Monte Carlo* method to choose a large numbers of sigma points. It came about from the geophysical sciences as an answer for the very large states and systems needed to model things such as the ocean and atmosphere. There is an interesting article on it's development in weather modeling in *SIAM News* [1]. The filter starts by randomly generating a large number of points distributed about the filter's initial state. This distribution is proportional to the filter's covariance $\\mathbf{P}$. In other words 68% of the points will be within one standard deviation of the mean, 95% percent within two standard deviations, and so on. Let's look at this in two dimensions. We will use `numpy.random.multivariate_normal()` function to randomly create points from a multivariate normal distribution drawn from the mean (5, 3) with the covariance\n",
    "\n",
    "$$\\begin{bmatrix}\n",
    "32 & 15 \\\\ 15 & 40\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "I've drawn the covariance ellipse representing two standard deviations to illustrate how the points are distributed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from numpy.random import multivariate_normal\n",
    "from filterpy.stats import (covariance_ellipse, \n",
    "                            plot_covariance_ellipse)\n",
    "\n",
    "mean = (5, 3)\n",
    "P = np.array([[32, 15],\n",
    "              [15., 40.]])\n",
    "\n",
    "x,y = multivariate_normal(mean=mean, cov=P, size=2500).T\n",
    "plt.scatter(x, y, alpha=0.3, marker='.')\n",
    "plt.axis('equal')\n",
    "\n",
    "plot_covariance_ellipse(mean=mean, cov=P,\n",
    "                        variance=2.**2,\n",
    "                        facecolor='none')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As I already stated, when the filter is initialized a large number of sigma points are drawn from the initial state ($\\mathbf{x}$) and covariance ($\\mathbf{P}$). From there the algorithm proceeds very similarly to the UKF. During the prediction step the sigma points are passed through the state transition function, and then perturbed by adding a bit of noise to account for the process noise. During the update step the sigma points are translated into measurement space by passing them through the measurement function, they are perturbed by a small amount to account for the measurement noise. The Kalman gain is computed from the \n",
    "\n",
    "We already mentioned the main difference between the UKF and EnKF - the UKF choses the sigma points deterministically. There is another difference, implied by the algorithm above. With the UKF we generate new sigma points during each predict step, and after passing the points through the nonlinear function we reconstitute them into a mean and covariance by using the *unscented transform*. The EnKF keeps propagating the originally created sigma points; we only need to compute a mean and covariance as outputs for the filter! \n",
    "\n",
    "Let's look at the equations for the filter. As usual, I will leave out the typical subscripts and superscripts; I am expressing an algorithm, not mathematical functions. Here $N$ is the number of sigma points, $\\chi$ is the set of sigma points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialize Step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\boldsymbol\\chi \\sim \\mathcal{N}(\\mathbf{x}_0, \\mathbf{P}_0)$$\n",
    "\n",
    "This says to select the sigma points from the filter's initial mean and covariance. In code this might look like\n",
    "\n",
    "```python\n",
    "N = 1000\n",
    "sigmas = multivariate_normal(mean=x, cov=P, size=N)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predict Step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{aligned}\n",
    "\\boldsymbol\\chi &= f(\\boldsymbol\\chi, \\mathbf{u}) + v_Q \\\\\n",
    "\\mathbf{x} &= \\frac{1}{N} \\sum_1^N \\boldsymbol\\chi\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "That is short and sweet, but perhaps not entirely clear. The first line passes all of the sigma points through a use supplied state transition function and then adds some noise distributed according to the $\\mathbf{Q}$ matrix. In Python we might write\n",
    "\n",
    "```python\n",
    "for i, s in enumerate(sigmas):\n",
    "    sigmas[i] = fx(x=s, dt=0.1, u=0.)\n",
    "\n",
    "sigmas += multivariate_normal(x, Q, N)\n",
    "```\n",
    "\n",
    "The second line computes the mean from the sigmas. In Python we will take advantage of `numpy.mean` to do this very concisely and quickly.\n",
    "\n",
    "```python\n",
    "x = np.mean(sigmas, axis=0)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now optionally compute the covariance of the mean. The algorithm does not need to compute this value, but it is often useful for analysis. The equation is\n",
    "\n",
    "$$\\mathbf{P} = \\frac{1}{N-1}\\sum_1^N[\\boldsymbol\\chi-\\mathbf{x}^-][\\boldsymbol\\chi-\\mathbf{x}^-]^\\mathsf{T}$$\n",
    "\n",
    "$\\boldsymbol\\chi-\\mathbf{x}^-$ is a one dimensional vector, so we will use `numpy.outer` to compute the $[\\boldsymbol\\chi-\\mathbf{x}^-][\\boldsymbol\\chi-\\mathbf{x}^-]^\\mathsf{T}$ term. In Python we might write\n",
    "\n",
    "```python\n",
    "    P = 0\n",
    "    for s in sigmas:\n",
    "        P += outer(s-x, s-x)\n",
    "    P = P / (N-1)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Update Step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the update step we pass the sigma points through the measurement function, compute the mean and covariance of the sigma points, compute the Kalman gain from the covariance, and then update the Kalman state by scaling the residual by the Kalman gain. The equations are\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\boldsymbol\\chi_h &= h(\\boldsymbol\\chi, u)\\\\\n",
    "\\mathbf{z}_{mean} &= \\frac{1}{N}\\sum_1^N \\boldsymbol\\chi_h \\\\ \\\\\n",
    "\\mathbf{P}_{zz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi_h - \\mathbf{z}_{mean}][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T} + \\mathbf{R} \\\\\n",
    "\\mathbf{P}_{xz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi - \\mathbf{x}^-][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T} \\\\\n",
    "\\\\\n",
    "\\mathbf{K} &= \\mathbf{P}_{xz} \\mathbf{P}_{zz}^{-1}\\\\ \n",
    "\\boldsymbol\\chi & = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\boldsymbol\\chi_h + \\mathbf{v}_R] \\\\ \\\\\n",
    "\\mathbf{x} &= \\frac{1}{N} \\sum_1^N \\boldsymbol\\chi \\\\\n",
    "\\mathbf{P} &= \\mathbf{P} - \\mathbf{KP}_{zz}\\mathbf{K}^\\mathsf{T}\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is very similar to the linear KF and the UKF. Let's just go line by line.\n",
    "\n",
    "The first line,\n",
    "\n",
    "$$\\boldsymbol\\chi_h = h(\\boldsymbol\\chi, u),$$\n",
    "\n",
    "just passes the sigma points through the measurement function $h$. We name the resulting points $\\chi_h$ to distinguish them from the sigma points. In Python we could write this as\n",
    "\n",
    "```python\n",
    "sigmas_h = h(sigmas, u)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next line computes the mean of the measurement sigmas.\n",
    "\n",
    "$$\\mathbf{z}_{mean} = \\frac{1}{N}\\sum_1^N \\boldsymbol\\chi_h$$\n",
    "\n",
    "In Python we write\n",
    "\n",
    "```python\n",
    "z_mean = np.mean(sigmas_h, axis=0)\n",
    "```\n",
    "    \n",
    "Now that we have the mean of the measurement sigmas we can compute the covariance for every measurement sigma point, and the *cross variance* for the measurement sigma points vs the sigma points. That is expressed by these two equations\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbf{P}_{zz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi_h - \\mathbf{z}_{mean}][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T} + \\mathbf{R} \\\\\n",
    "\\mathbf{P}_{xz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi - \\mathbf{x}^-][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T}\n",
    "\\end{aligned}$$\n",
    "\n",
    "We can express this in Python with\n",
    "\n",
    "```python\n",
    "P_zz = 0\n",
    "for sigma in sigmas_h:\n",
    "    s = sigma - z_mean\n",
    "    P_zz += outer(s, s)\n",
    "P_zz = P_zz / (N-1) + R\n",
    "\n",
    "P_xz = 0\n",
    "for i in range(N):\n",
    "    P_xz += outer(self.sigmas[i] - self.x, sigmas_h[i] - z_mean)\n",
    "P_xz /= N-1\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Computation of the Kalman gain is straightforward $\\mathbf{K} = \\mathbf{P}_{xz} \\mathbf{P}_{zz}^{-1}$.\n",
    "\n",
    "In Python this is\n",
    "\n",
    "```python\n",
    "K = P_xz @ inv(P_zz)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we update the sigma points with\n",
    "\n",
    "$$\\boldsymbol\\chi  = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\boldsymbol\\chi_h + \\mathbf{v}_R]$$ \n",
    "\n",
    "Here $\\mathbf{v}_R$ is the perturbation that we add to the sigmas. In Python we can implement this with\n",
    "\n",
    "```python\n",
    "v_r = multivariate_normal([0]*dim_z, R, N)\n",
    "for i in range(N):\n",
    "    sigmas[i] += K @ (z + v_r[i] - sigmas_h[i])\n",
    "```\n",
    "\n",
    "\n",
    "Our final step is recompute the filter's mean and covariance.\n",
    "\n",
    "```python\n",
    "    x = np.mean(sigmas, axis=0)\n",
    "    P = self.P - K @ P_zz @ K.T\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation and Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I have implemented an EnKF in the `FilterPy` library. It is in many ways a toy. Filtering with a large number of sigma points gives us very slow performance. Furthermore, there are many minor variations on the algorithm in the literature. I wrote this mostly because I was interested in learning a bit about the filter. I have not used it for a real world problem, and I can give no advice on using the filter for the large problems for which it is suited. Therefore I will refine my comments to implementing a very simple filter. I will use it to track an object in one dimension, and compare the output to a linear Kalman filter. This is a filter we have designed many times already in this book, so I will design it with little comment. Our state vector will be\n",
    "\n",
    "$$\\mathbf{x} = \\begin{bmatrix}x\\\\ \\dot{x}\\end{bmatrix}$$\n",
    "\n",
    "The state transition function is\n",
    "\n",
    "$$\\mathbf{F} = \\begin{bmatrix}1&1\\\\0&1\\end{bmatrix}$$\n",
    "\n",
    "and the measurement function is\n",
    "\n",
    "$$\\mathbf{H} = \\begin{bmatrix}1&0\\end{bmatrix}$$\n",
    "\n",
    "The EnKF is designed for nonlinear problems, so instead of using matrices to implement the state transition and measurement functions you will need to supply Python functions. For this problem they can be written as:\n",
    "\n",
    "```python\n",
    "def hx(x):\n",
    "    return np.array([x[0]])\n",
    "\n",
    "def fx(x, dt):\n",
    "    return F @ x\n",
    "```\n",
    "\n",
    "One final thing: the EnKF code, like the UKF code, uses a single dimension for $\\mathbf{x}$, not a two dimensional column matrix as used by the linear kalman filter code.\n",
    "\n",
    "Without further ado, here is the code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import kf_book.book_plots as bp\n",
    "from numpy.random import randn\n",
    "from filterpy.kalman import EnsembleKalmanFilter as EnKF\n",
    "from filterpy.kalman import KalmanFilter\n",
    "from filterpy.common import Q_discrete_white_noise\n",
    "\n",
    "np.random.seed(1234)\n",
    "\n",
    "def hx(x):\n",
    "    return np.array([x[0]])\n",
    "\n",
    "def fx(x, dt):\n",
    "    return F @ x\n",
    "    \n",
    "F = np.array([[1., 1.],[0., 1.]])\n",
    "\n",
    "x = np.array([0., 1.])\n",
    "P = np.eye(2) * 100.\n",
    "enf = EnKF(x=x, P=P, dim_z=1, dt=1., N=20, hx=hx, fx=fx)\n",
    "\n",
    "std_noise = 10.\n",
    "enf.R *= std_noise**2\n",
    "enf.Q = Q_discrete_white_noise(2, 1., .001)\n",
    "\n",
    "kf = KalmanFilter(dim_x=2, dim_z=1)\n",
    "kf.x = np.array([x]).T\n",
    "kf.F = F.copy()\n",
    "kf.P = P.copy()\n",
    "kf.R = enf.R.copy()\n",
    "kf.Q = enf.Q.copy()\n",
    "kf.H = np.array([[1., 0.]])\n",
    "\n",
    "measurements = []\n",
    "results = []\n",
    "ps = []\n",
    "kf_results = []\n",
    "\n",
    "zs = []\n",
    "for t in range (0,100):\n",
    "    # create measurement = t plus white noise\n",
    "    z = t + randn()*std_noise\n",
    "    zs.append(z)\n",
    "\n",
    "    enf.predict()\n",
    "    enf.update(np.asarray([z]))\n",
    "    \n",
    "    kf.predict()\n",
    "    kf.update(np.asarray([[z]]))\n",
    "\n",
    "    # save data\n",
    "    results.append (enf.x[0])\n",
    "    kf_results.append (kf.x[0,0])\n",
    "    measurements.append(z)\n",
    "    ps.append(3*(enf.P[0,0]**.5))\n",
    "\n",
    "results = np.asarray(results)\n",
    "ps = np.asarray(ps)\n",
    "\n",
    "plt.plot(results, label='EnKF')\n",
    "plt.plot(kf_results, label='KF', c='b', lw=2)\n",
    "bp.plot_measurements(measurements)\n",
    "plt.plot (results - ps, c='k',linestyle=':', lw=1, label='1$\\sigma$')\n",
    "plt.plot(results + ps, c='k', linestyle=':', lw=1)\n",
    "plt.fill_between(range(100), results - ps, results + ps, facecolor='y', alpha=.3)\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be a bit difficult to see, but the KF and EnKF start off slightly different, but soon converge to producing nearly the same values. The EnKF is a suboptimal filter, so it will not produce the optimal solution that the KF produces. However, I deliberately chose $N$ to be quite small (20) to guarantee that the EnKF output is quite suboptimal. If I chose a more reasonable number such as 2000 you would be unable to see the difference between the two filter outputs on this graph."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Outstanding Questions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All of this should be considered as *my* questions, not lingering questions in the literature. However, I am copying equations directly from well known sources in the field, and they do not address the discrepancies.\n",
    "\n",
    "First, in Brown [2] we have all sums multiplied by $\\frac{1}{N}$, as in \n",
    "\n",
    "$$ \\hat{x} = \\frac{1}{N}\\sum_{i=1}^N\\chi_k^{(i)}$$\n",
    "\n",
    "The same equation in Crassidis [3] reads (I'll use the same notation as in Brown, although Crassidis' is different)\n",
    "\n",
    "$$ \\hat{x} = \\frac{1}{N-1}\\sum_{i=1}^N\\chi_k^{(i)}$$\n",
    "\n",
    "The same is true in both sources for the sums in the computation for the covariances. Crassidis, in the context of talking about the filter's covariance, states that $N-1$ is used to ensure an unbiased estimate. Given the following standard equations for the mean and standard deviation (p.2 of Crassidis), this makes sense for the covariance.\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mu &= \\frac{1}{N}\\sum_{i=1}^N[\\tilde{z}(t_i) - \\hat{z}(t_i)] \\\\\n",
    " \\sigma^2 &= \\frac{1}{N-1}\\sum_{i=1}^N\\{[\\tilde{z}(t_i) - \\hat{z}(t_i)] - \\mu\\}^2\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "However, I see no justification or reason to use $N-1$ to compute the mean. If I use $N-1$ in the filter for the mean the filter does not converge and the state essentially follows the measurements without any filtering. However, I do see a reason to use it for the covariance as in Crassidis, in contrast to Brown. Again, I support my decision empirically - $N-1$ works in the implementation of the filter, $N$ does not.\n",
    "\n",
    "My second question relates to the use of the $\\mathbf{R}$ matrix. In Brown $\\mathbf{R}$ is added to $\\mathbf{P}_{zz}$ whereas it isn't in Crassidis and other sources. I have read on the web notes by other implementers that adding R helps the filter, and it certainly seems reasonable and necessary to me, so this is what I do. \n",
    "\n",
    "My third question relates to the computation of the covariance $\\mathbf{P}$. Again, we have different equations in Crassidis and Brown. I have chosen the implementation given in Brown as it seems to give me the  behavior that I expect (convergence of $\\mathbf{P}$ over time) and it closely compares to the form in the linear KF. In contrast I find the equations in Crassidis do not seem to converge much.\n",
    "\n",
    "My fourth question relates to the state estimate update. In Brown we have \n",
    "\n",
    "$$\\boldsymbol\\chi  = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\mathbf{z}_{mean} + \\mathbf{v}_R]$$ \n",
    "\n",
    "whereas in Crassidis we have\n",
    "\n",
    "$$\\boldsymbol\\chi  = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\boldsymbol\\chi_h + \\mathbf{v}_R]$$ \n",
    "\n",
    "To me the Crassidis equation seems logical, and it produces a filter that performs like the linear KF for linear problems, so that is the formulation that I have chosen. \n",
    "\n",
    "I am not comfortable saying either book is wrong; it is quite possible that I missed some point that makes each set of equations work. I can say that when I implemented them as written I did not get a filter that worked. I define \"work\" as performs essentially the same as the linear KF for linear problems. Between reading implementation notes on the web and reasoning about various issues I have chosen the implementation in this chapter, which does in fact seem to work correctly. I have yet to explore the significant amount of original literature that will likely definitively explain the discrepancies. I would like to leave this here in some form even if I do find an explanation that reconciles the various differences, as if I got confused by these books than probably others will as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [1] Mackenzie, Dana. *Ensemble Kalman Filters Bring Weather Models Up to Date* Siam News,  Volume 36, Number 8, October 2003. http://www.siam.org/pdf/news/362.pdf\n",
    "\n",
    "- [2]  Brown, Robert Grover, and Patrick Y.C. Hwang. *Introduction to Random Signals and Applied Kalman Filtering, With MATLAB® excercises and solutions.* Wiley, 2012.\n",
    "\n",
    "- [3] Crassidis, John L., and John L. Junkins. *Optimal estimation of dynamic systems*. CRC press, 2011."
   ]
  }
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